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Contest: Task: Related: TaskB TaskD

Score : $300$ points

Problem Statement

There are $N$ dishes arranged in a row in front of Takahashi. The $i$-th dish from the left has $A_i$ oranges on it.

Takahashi will choose a triple of integers $(l, r, x)$ satisfying all of the following conditions:

  • $1\leq l \leq r \leq N$;
  • $1 \le x$;
  • for every integer $i$ between $l$ and $r$ (inclusive), $x \le A_i$.

He will then pick up and eat $x$ oranges from each of the $l$-th through $r$-th dishes from the left.

At most how many oranges can he eat by choosing the triple $(l, r, x)$ to maximize this number?

Constraints

  • All values in input are integers.
  • $1 \leq N \leq 10^4$
  • $1 \leq A_i \leq 10^5$

Input

Input is given from Standard Input in the following format:

$N$
$A_1$ $\ldots$ $A_N$

Output

Print the maximum number of oranges Takahashi can eat.

Sample Input 1

6
2 4 4 9 4 9

Sample Output 1

20

By choosing $(l,r,x)=(2,6,4)$, he can eat $20$ oranges.

Sample Input 2

6
200 4 4 9 4 9

Sample Output 2

200

By choosing $(l,r,x)=(1,1,200)$, he can eat $200$ oranges.